Towards a New Form of National Impedance

Standard for Millimetre Wavelengths using

Dielectric Waveguide

Jimmy Yip1, M-H John Lee2, Nick Ridler1, and Richard Collier2

1 NPL2 Cavendish Laboratory, University of Cambridge

Drawbacks in Metallic Waveguides

• Skin effect

• Surface roughness to

• Mono-mode operation

• Narrow band in metallic rectangular waveguide

21−∝ fα

f∝α

23f∝α 25f

Types of Dielectric Waveguide

1rε0ε

(a)

Circular dielectric rod

guide (variants: elliptical

dielectric rod guide)

0ε

1rε

(b)

Rectangular dielectric

rod guide

0ε

1rε

Ground Plane

(c)

Image guide (d)

Insulated image guide

(variants: strip guide – an

un-grounded insulated

image guide)

0ε

2rε

Ground Plane

1rε

0ε

1rε

Ground Plane

(e)

Grounded rib waveguide

(variants: un-grounded

ridge guide)

(f)

Embedded stripline

(variants: optical fibre – a

fully embedded circular

dielectric rod, and trapped

image guide)

0rε

1rε2rε

(g)

2D Photonic Crystal Structure

(Periodic discontinuities cause matched-

multiple-reflections, which form a “photonic

bandgap” or virtual cut-off. It can be

developed into 2D or 3D wave guiding

structures. Variants: circular photonic crystal

fibre, etc.)

Guided

Wave

Multiple reflections

0rε

1rε (h) Dielectric slab guide: one of the dimensions at the

cross-section is extended to infinite. (This physically

unrealisable guide is only used for the field and wave

analysis, e.g. a rectangular dielectric rod guide can be

mathematically approximated by the combination of

two slab guides perpendicular to each other.)

0ε

1rε

Ray trace in a rectangular dielectric rod waveguide. ( )12 εε >

A

B

C D

A’

B’

C’

2ε1εx

z

y

A

B

C

D

A’

B’

C’ z

y

A

B

C

D

A’

B’

C’

x

z

The zigzagging wave is bounced off from each of the four walls sequentially within the rectangular dielectric rod

guide under internal reflection

Propagation modes in dielectric waveguide

a2

b21rε 2rε

x

y

a2

1rε

2rε

1rε

xE

TM10 ModeTE01 Mode

1rε

2rε

1rε

b2xE

(1) The x

E11 mode in a rectangular dielectric rod waveguide is the combination of the TM10 and TE01modes in dielectric slab guides.

yE

a2

1rε

2rε

1rε

TE10 Mode

1rε

2rε

1rε

b2 yE

TM01 Mode

(2) The yE11 mode can be treated as the combination of the TE10 and TM01 modes.

There are two dominant

modes in dielectric

waveguide: Ex and Ey modes

Selection of dielectric materials

V. Good1170.0002 @ 1 kHz2.12 @ 1 MHzTPX(Polymethylpentene)

V. Poor100 –2000.0001 – 0.001 @ 1 MHz

2.3 – 2.4 @ 1 MHz

HDPE(High Density Polyethylene)

Fair100 –1800.0003 – 0.0005 @ 1 MHz

2.2 – 2.6 @ 1 MHz

PP(Polypropylene)

V. Good70 – 900.0002 @ 1 MHz2.5 @ 1 MHzRexolite(Cross-link Polystyrene)

Poor100 –1600.0003 – 0.0007 @ 1 MHz

2.0 – 2.1 @ 1 MHz

PTFE(Polytetrafluoroethylene)

Good47/1080.003 @ 1 MHz3.2 to 3.3 @ 50 Hz – 10 kHz

PEEK(Polyetheretherketone)

RigidityCoefficient of Thermal Expansion

( x10-6 K-1)

Dissipation Factor

tanδ

Dielectric Constant

ε

Name

Measurement of different dielectric materials 1

Comparing Different Dielectric Materials

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

75 80 85 90 95 100 105 110

Frequency (GHz)

S21 (

dB

)

PP

PTFE

HDPE

Rexolite

PEEK

TPX

Measurement of different dielectric materials 2

-3

-2.5

-2

-1.5

-1

-0.5

0

75 80 85 90 95 100 105 110

Frequency (GHz)

S21 (

dB

)

PP HDPE

Rexolite TPX

Tapered transition

Rectangular

Waveguide

Taper

Section

Dielectric-filled Rectangular

Waveguide

a=2540µm

b=1270µm

x

zy

E

Port 1

Port 2

Different types of taper

(a) H-Plane Asymmetric Taper. (b) H-Plane Symmetric Taper. (c) E-Plane Asymmetric Taper.

(d) E-Plane Symmetric Taper. (e) Pyramidal Taper. (Tapered in both

H- and E-planes)

Simulation result of different tapers

-60

-50

-40

-30

-20

-10

0

75 80 85 90 95 100 105 110

Frequency (GHz)

S1

1 (

dB

)

No Taper (a) (b) (c) (d) (e)

(a) H-plane asymmetric

(b) H-plane symmetric

(c) E-plane asymmetric

(d) E-plane symmetric

(e) Pyramidal

Field analysis in different tapers

(a) Asymmetric H-plane taper.

Ray Trace

0ε

E

a

Taper Length (TL)

2.3=rεα

1η 2η

(b) Symmetric H-plane taper.

E

2.3=rε0ε

α

1η

2η

E-field

E 2.3=rε

b

0ε

1λ 2λ

(c) E-plane asymmetric taper.

2.3=rε0ε

1λ 2λ

(d) E-plane symmetric taper.

Standard wheel

Measurement of different off-set shorts 1

Measured in an un-calibrated system

75 GHz

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Real

Imag

inary

Short

2.435mm

3.632mm

4.561mm

5.100mm

5.590mm

110 GHz

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Real

Imag

inary

Short

2.435mm

3.632mm

4.561mm

5.100mm

5.590mm

Measurement of different off-set shorts 2

92.5 GHz

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Real

Imag

inary

Short

2.435mm

3.632mm

4.561mm

5.100mm

5.590mm

96 GHz

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Real

Imag

inary

Short

2.435mm

3.632mm

4.561mm

5.100mm

5.590mm

Calibration using 4 standards

Uncertainty profile

Expected size of errors in |S11| at 75 GHz

Transmission mediumRandom errors due to

connection repeatability

Systematic errors due to

connection misalignment

Combined standard

uncertainty

Dielectric Waveguide 0.003 0.002 0.003

Rectangular Metallic

Waveguide

0.007 0.006 0.008

Conclusions

• Lower loss

• Better connectivity (even with small air gap)

• Good repeatability

• It can be used on integrated waveguides and photonic

band-gap structures